Locally Repairable and Locally Regenerating Codes Obtained by Parity-Splitting of HashTag Codes

We construct an explicit family of locally repairable and locally regenerating codes whose existence was proven in a recent work by Kamath et al. about codes with local regeneration (but no explicit construction was given). This explicit family of codes is based on HashTag codes. HashTag codes are recently defined vector codes with different vector length $\alpha$ (also called a sub-packetization level) that achieve the optimal repair bandwidth of MSR codes or near-optimal repair bandwidth depending on the sub-packetization level. We applied the technique of parity-splitting code construction. Additionally, we show that the lower bound on the size of the finite field where these codes are constructed, given in the same work of Kamath et al., can be lower. Finally, we discuss the importance of having two ways for node repair with locally regenerating HashTag codes: repair only with local parity nodes or repair with both local and global parity nodes. To the best of the authors' knowledge, this is the first work where this is discussed. Namely, we give a practical example where several optimization metrics such as the repair bandwidth, the number of I/O operations, the access time for the contacted parts and the size of the stored file determine the repair procedure.